Well, regardless of whatever other plotting among each other, all participants actually do have a very good reason to join—their kids still go to Hogwarts, they want to keep them safe but at the same time groom them to inherit the family fortunes, and as was pointed out explicitly in the chapter, there are still good reasons, both politically and for safety, not to go to the other schools. An (at least temporary) alliance for the protection of their children is actually quite logical for all concerned.